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| Research on linear dependence problem of numerical manifold method |
| Received:June 02, 2011 Revised:September 19, 2011 |
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| DOI：10.7511/jslx20125019 |
| KeyWord:numerical manifold method linear dependence partition of unity finite covers covers function local approximate function generalized FEM |
| Author | Institution |
| 林毅峰 |
同济大学 岩土及地下工程教育部重点实验室 土木工程学院 地下建筑与工程系, 上海 ;上海勘测设计研究院, 上海 |
| 朱合华 |
同济大学 岩土及地下工程教育部重点实验室 土木工程学院 地下建筑与工程系, 上海 |
| 蔡永昌 |
同济大学 岩土及地下工程教育部重点实验室 土木工程学院 地下建筑与工程系, 上海 |
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| Abstract: |
| The shape function of Numerical Manifold Method(NMM) is composed of cover functions and local approximate functions.The shape functions of NMM are prone to Linear Dependent (LD).The LD problem was investigated.It is indicated that the origin of LD comes from partition of unity of local cover functions and LD is dependent of the shape of element.The relationship among LD of shape function,nullity of global stiffness matrices and convergence of solution was researched,and it revealed that the LD of shape functions is not inevitably null of global stiffness matrices.The relationship between local approximate polynomial function and LD of eight-node hexahedron manifold element was also analyzed and a linear independency element was devised.The effect of full first-order polynomial local approximate functions on calculation accuracy and convergence was investigated with case calculations.It indicated that the solution of full first-order polynomial local approximate functions is convergent although it is linear dependent,and it is more accurate than the linear independence element. |